计算1-½-1/2^2-1/2^3-……-1/2^2009

问题描述:

计算1-½-1/2^2-1/2^3-……-1/2^2009

1-½-1/2^2-1/2^3-……-1/2^2009
=1-(½+1/2^2+1/2^3+……+1/2^2009)
= 1-(1-1/2^2009)
=1/2^2009